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Question

The angles of the ΔABC and ΔDEF are given as follows;

A=90, B=30, D=90, and E=30
If the side BC is twice the side EF, which of the following statement is true?

A
sinB=2sinE
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B
sinE=2sinB
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C
sinB=sinE
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D
sinA=sinB
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Solution

The correct option is C sinB=sinE
In ABC
A=90 , B=30

We have, A+B+C=180
C=1809030= 60

Similarly,
In DEF
D=90 , E=30

We have, D+E+F=180
F=1809030= 60

In ABC and DEF

A=D=90
B=E=30
C=F=60

Three corresponding pair of angles are equal. Hence both triangles are similar.
BCEF=ABDE=ACDF

Consider,
BCEF=ACDF

BCAC=EFDF

sinB=sinE

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